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This study considers the control of spherical robot linear motion under input saturation. A fractional sliding mode controller that combines fractional order calculus and the hierarchical sliding mode control method is proposed for the spherical robot. Employing this controller, an auxiliary system in which a filter was used to gain smooth control performance was designed to overcome the input saturation. Based on the Lyapunov stability theorem, the closed-loop system was globally stable and the desired state was achieved using the fractional sliding mode controller. The advantages of the proposed controller are illustrated by comparing the simulation results from the fractional order sliding mode controllers and the integer order controller.

Smooth Fractional Order Sliding Mode Controller for Spherical Robots with Input Saturation